MOSFET review

andShort channel effects in FETs With current channel lengths of 120/45 nm and industry pushing towards 32 nm, classical approaches to describe the functioning of the devices are not good enough.

Outline

Some history Basic transport equations MOSFET theory – review Currents derived from the inversion charge QI Expression for the threshold voltage Why downscale the MOSFET? Short channel effects Other parameters that influence the behaviour

5 Field effect • Channel is NOT created by injection of carriers via the 3rd contact but is created by the attraction- repulsion of charges via an electric field • Control of enhancement and depletion of the carriers in the channel via capacitive effect • Current through 3rd contact very very small IG≈0.

Charge sheet model

drift & diffusion currentsThe general solution of carrier transport through the MOSFET relies on the expression forthe inversion charge. The assumption is that the inversion layer is of infinitesimal thickness.

Vs(x) Vs(x+∆x) Inversion layer I(x)

x x+∆x

The inversion charge QI is derived in terms of surface potential Vs

What is the surface potential?

9 Intrinsic level For an intrinsic semiconductor the Fermi level is equal to the intrinsic level. Or: for EF=Ei, n=niEnergy

If φm ≠ φs − QdeplVth = (φm − φs ) + + 2φF CoxIf there is a workfunction difference between metal and semiconductor, then thisdifference needs to be removed before the previous analysis can be done →introduction of first term.

Influence of the bulk doping on Vth

These bulk charges QB however will lead to a depletion width

and thus capacitance that will change from source to drain. This will influence the threshold voltage and will change the shape of the I-V characteristics → body effect

m ox inv QB p-Si

Threshold voltage – review (interpretation)

MOS junction a) Initial band bending due to workfunction difference between gate and semiconductor. EC Thus apply VG=φG-φs=VFB for flat band. Ei b) For threshold voltage apply gate voltageEFG φF EFs to flat band condition such that channel is as EV much n-type as substrate is p-type. VT1=VFB-2φF (with this sign φF = EF-Ei) oxide

But fixed negative charges QB in the depletion layer will “screen”

the electrons that need to be attracted from the substrate, so an extra gate voltage needs to be applied Amount of charge in depletion region: QB Thus changes threshold voltage: VT2=VFB-2φF -QB/Cox

17 I-V shape – influence of Vth on currentLong channel MOSFET The depletion charge QB is taken constant along the whole channel length. The potential in the channel from source to drain is a linear function of VGS-VT1-Vx(x)

I = Cox (VGS –Vx(x) – VT1) W µe dVx/dx

VT1=VFB-2φF Or VT1=VFB-2φF -QB/Cox

Approximation: depletion width constant

But: depletion width along the channel

length not constant (VDS)

NA- NA-

Thus QB in the depletion layer is not constant along the channel

I = Cox (VGS –Vx(x) – VT2 (x) ) W µe dVx/dx VT2=VFB-2φF –QB(x)/Cox

QB ( x) = 2qN Aε Si (2φ F + Vx ( x))

L − ∆L ( 2φ F ,Vx ( x )) QB = − ∫ 2qN Aε Si ( 2φ F + Vx ( x)) 0+

18 Influence of substrate on depletion region and thus on the threshold voltage

Influences depletion/enhancement effects from “substrate”

Space charge region controlled not only by the gate but also by the drain-substrate reverse bias.

QB = − 2qN Aε Si ( 2φ F + Vx ( x) − Vbulk )

Influence of gate oxide charges

Charges in oxide Assuming we can represent the charges in the oxide and the charges at the interface of oxide and semiconductor (interface charge density) as an effective positive charge Qi, then this charge inside the oxide will cause bandbending which will need to be taken into account in the threshold voltage. VT=VFB-2φF -QB/Cox -Qi/Cox Sign convention

Speed Packing density

Price per transistor Factory costs

105 Factory costs (M USD)

1 Price (USdollar)

10-7 1970 2002 10 1975 2005

21 Short channel effectsLong ago, MOSFETs were big and could be described via drift currents and carrier control via the gate capacitanceNow MOSFETs are small in order to increase their operation speed. Pushing the dimensions of the gate length down influences the electrostatics of the devices.In order to preserve the electrostatic integrity of the MOSFET scaling has proceeded in a controlled way:Lg ↓ has to go together with tox ↓, NA ↑, tj ↓, VDD ↓ and W ↓But reducing these geometrical parameters not only increases fabrication complexity but also change the physical processes in the device

short channel effects

AimTo understand what short channel effects are and where they come from.To investigate ways in which to minimise short channel effects

22 Gate length modulation

Due to pinch off, the effective gate length reduces

L ∆L

∆L

1 1 I DS ∝ → I DS ∝ L L − ∆L λ channel length modulation coefficient

Source and drain depletion regions

formed by pn-junctionsDraw the energy band diagram between the source and the drain for differentgate voltages. L

n n Leff p

depletion depletion

23 Relative importance of source and drain depletion regions Due to depletion widths from source and drain area extending towards the centre of the channel. The extend of the depletion width becomes comparable to the original gate length in short channel FETs. L L

Ideally QB bulk charge

24 Assumptions made in order to derive an analytical model for the Vth roll-off.

• VDS=0V • S & D implanted regions are circular near the channel • The implant depth of the S & D ohmic contacts, tj are the same • The depletion layers WSB, WDB and Wdepl are all the same width. • The charges at the S & D are equally shared with the gate.

To limit threshold voltage roll-off:

Drain Induced Barrier Lowering (DIBL)

Gate controls source barrier: Simple principle: when the gate voltage is low, an energy barrier prevents electrons from flowing from source to drain. A higher gate voltage lowers the energy barrier, allowing more current to flow.

S D Drain controls source barrier:

Ideally only gate controls the barrier height. For small MOSFETs, the drain voltage lowers the barrier between source and channel. Loss of gate control

Strategies to control short-channel

Controls the extension of the depletion width and controls

the influence of the bulk on the threshold voltage without influencing the mobility in the channel via high impurity scattering.

30 Other parametersOther parameters that influence the current-voltage characteristics that we have not yettaken into account.

Mobility variations + ED

S + D

n+ n+ S D EG EGD Due to scattering (function of resulting field), there is aField on the carriers in variation of the mobility inthe channel is composed the channelof 2 componentsVariation of resultingfield along the channel

MOS in weak inversion = Parasitic BJT

Gate Cox with “base” controlled via capacitive divider. Source Drain

Cdepl Bulk (p)

The S-B-D = npn sandwich with mobile minority carriers in the p-type bulk region. This is equivalent to a BJT, except that the base potential is controlled through a capacitive divider Cox and Cdepl, and not directly by carrier injection via the third electrode.

When this volume is very small, due to the statistical

distribution of the doping atoms, the bulk doping might be different from device to device.

Dopants in a small transistor.

3D simulation of a 30 nm by 30 nm field-effect transistor domain that contains random discrete dopants in the source, drain, and substrate (bulk).The electrostatic potential is color-mapped from red (1 V) through the rainbow to blue (0 V). Potential fluctuations in the channel associated with the random distribution of dopants result in differing characteristics for each device. (Top inset) Schematic diagram of the basic interconnect wiring structure of a field-effect transistor. (Bottom inset) Circuit diagram symbol for a field-effect transistor. CREDIT:A. BROWN/UNIVERSITY OF GLASGOW Ref. Roy, Asenov, Where do dopants go? Science magazine.

38 Conclusion• Different short channel effects contribute to a deviation of the current-voltage characteristics based on the “simple” MOSFET model: DIBL and leakage currents are the main culprits.• Present day devices need more ingenious models. – 2-D and 3-D device simulators are commercially available • MEDICI, TAURUS • ATLAS• We need novel device geometries or material systems to deal with these problems.